Question

A group of 25 particles have the following speeds: two have speed 11m/s , seven have 16m/s , four have 22m/s , three have 25m/s , six have 31m/s , one has 34m/s , and two have 41 m/s .
a. Determine the average speed.
vavg= ______________m/s
b. Determine the rms speed.
vrms= ______________m/s
c. Determine the most probable speed.

Answer 1

Answer:

a) vavg = 16.59 m/s

b) vrms= 26.42 m/s

c) the most probable speed is the average speed = 16.59 m/s  (since the is no particle with 16.59 m/s → 16m/s is the most probable speed observed)

Explanation:

a) the average velocity will be

vavg =( 1/total number of particles )*∑ velocity * number of particles  

= (2*11 + 4*16 + 4*22 +3*25 + 6*31  + 1*34 + 2*41)/ (2 + 4 + 4 +3 + 6 + 1 + 2) = 16.59 m/s

b) the root mean squared speed (rms) will be

vrms=√[( 1/total number of particles )*∑ velocity² * number of particles] =   √[ (2*11² + 4*16² + 4*22² +3*25² + 6*31²  + 1*34² + 2*41²)/ (2 + 4 + 4 +3 + 6 + 1 + 2)]  = 26.42 m/s

c) if any particle is chosen at random then the probability of choosing that particle will be the given be the fraction of particles over the total , and thus the expected speed (most probable speed ) will be the average speed = 16.59 m/s ( since the is no particle with 16.59 m/s → 16m/s is the most probable speed observed)